{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "sns.set_style(\"whitegrid\")\n",
    "sns.set(font_scale=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: divide by zero encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob = np.arange(0, 1.0, 0.001)\n",
    "odds = prob / (1-prob)\n",
    "logits = np.log(odds)\n",
    "\n",
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))\n",
    "ax1.plot(prob, logits, lw=3)\n",
    "ax1.set_xlabel('Probability')\n",
    "ax1.set_ylabel('Logit')\n",
    "#ax1.set_title('L vs. P(Y)')\n",
    "\n",
    "ax2.plot(logits, prob, lw=3)\n",
    "ax2.set_xlabel('Logit')\n",
    "ax2.set_ylabel('Probability')\n",
    "#ax2.set_title('P(Y) vs. L')\n",
    "\n",
    "ax3.plot(odds, logits, lw=3)\n",
    "ax3.set_xlabel('Odds')\n",
    "ax3.set_ylabel('Logit')\n",
    "#ax3.set_title('L vs. odds')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits[int(len(logits)/2)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "prob=0.9500000000000001 logit=2.944438979166442\n",
      "prob=0.995 logit=5.293304824724491\n",
      "prob=0.999 logit=6.906754778648553\n"
     ]
    }
   ],
   "source": [
    "x=len(logits)-50\n",
    "print('prob={} logit={}'.format(prob[x], logits[x]))\n",
    "x=len(logits)-5\n",
    "print('prob={} logit={}'.format(prob[x], logits[x]))\n",
    "x=len(logits)-1\n",
    "print('prob={} logit={}'.format(prob[x], logits[x]))"
   ]
  }
 ],
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